Advanced Solid State Physics

Table 3: Transition temperaturesTcfor some selected materials.

Material Tc/K

Ti 0. 4

Hg 4. 2

C 60 19. 2

Rb 2 CsC 60 19. 2

YBa 2 Cu 3 O 6. 9 90. 0

(Sn 5 In)Ba 4 Ca 2 Cu 10 Ox 212

16.2 Experimental Observations

16.2.1 Fundamentals

We already observed that superconductivity occurs in many metallic compounds, but also alloys, doped
semiconductors and even organic molecules. The transition temperaturesTcrange fromTc= 0. 001
K for Rh up toTc= 212K for (Sn 5 In)Ba 4 Ca 2 Cu 10 Ox. Some materials reach the phase transition
only under high pressure, for instance for Sip= 165kbar andTc= 8. 3 K. In Tab. 3 the transition
temperatures of some selected compounds are given. However, we can state that a material has to
be nonmagnetic in order to become a superconductor under appropriate conditions (in particular,
this statement is not true for highTcsuperconductors, which are based on cuprates). The question
whether every nonmagnetic material will become a superconductor at sufficiently low temperatures or
not, can fundamentally not be answered.

One of the earliest observations was that strong magnetic fields destroy superconductivity. The critical
field as a function of temperature,Hc(T)whereHc(Tc) = 0, separates the normal from the supercon-
ducting state, see Fig. 158. Note thatHc=μ^10 Bac, whereBacis the critical magnetic field andμ 0 is
the magnetic permeability of vacuum. The applied magnetic field will in the following be denoted by
Ba.

Since the superconducting state is destroyed above the critical magnetic field, there exists a maximum
current within the superconductor because a higher current would induce a magnetic field destroying
superconductivity. This maximum current is called critical currentJc. It can be estimated by equating
the energy of the critical magnetic field with kinetic energy ofnelectrons:

μ 0 Hc^2 ≈

1

2

nmev^2 , (263)

wheremeis the electron mass andvthe electron’s velocity. Since the current density can be written
asJ=−nqv(withqthe elementary charge) we obtain an estimate for the critical currentJcas a
function of the critical magnetic field

Jc≈

√

2 μ 0

q^2 nme

Hc. (264)